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Modeling Multi-Phase Systems Using Bond Graphs

Modeling Multi-Phase Systems Using Bond Graphs. Contents. Introduction Basic Model Determination of Variables Condensation on Cold Surfaces Model of a Pressure Cooker Conclusions. Basic Model. Ø. CD, DVA, Evaporation (and Condensation). Ø. 3. 3. 3. 3. CF. CF. gas. liq.

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Modeling Multi-Phase Systems Using Bond Graphs

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  1. Modeling Multi-Phase Systems Using Bond Graphs Jürgen Greifeneder, François Cellier

  2. Contents • Introduction • Basic Model • Determination of Variables • Condensation on Cold Surfaces • Model of a Pressure Cooker • Conclusions Jürgen Greifeneder, François Cellier

  3. Basic Model Ø CD, DVA, Evaporation (and Condensation) Ø 3 3 3 3 CF CF gas liq Jürgen Greifeneder, François Cellier

  4. Determination of Variables • State transition elements are modeled as special R-fields, however: • Mass flows are determined as a function of pressure and the corresponding saturation pressure • Volume flows are determined as the product of mass flow and the saturation volume at the corresponding temperature • Entropy flows will be superposed with enthalpy of evaporation Jürgen Greifeneder, François Cellier

  5. Condensation on Cold Surfaces Boundary layer CF CF Gas Gas Rand- schicht 3 3 CD DVA RF 3 3 . Ø Ø CD s S T 3 gas 3 Conduction (CD) Volume work (DVA) Condensation- and Evaporation Conduction (CD) Volume work (DVA) Condensation- and Evaporation CF 3 Ø Surface . s 3 T S 3 liq CD DVA RF 3 3 Ø Ø CD 3 3 CF CF liq liq Jürgen Greifeneder, François Cellier

  6. Model of a Pressure Cooker Air in Boundary layer SE: 393 K CD (t) CD DVA CD (t) Air RF: Dp CD (t) CD CD SE: 293 K CD DVA CD DVA Cond water CD CD steam RF: Dp CD (t) DVA Cond CD Steam in Boundary layer CD (t) Jürgen Greifeneder, François Cellier

  7. Pressure Cooker: Temperature Graph Jürgen Greifeneder, François Cellier

  8. Pressure Cooker: Pressure Graph Jürgen Greifeneder, François Cellier

  9. Conclusions • Phase transitions cannot be described in general without making assumptions • Simple phase transitions can now be modeled • This model accounts also for liquid within the gaseous phase and air bubbles within the fluid phase. • Condensation on cold surfaces can be modeled easily. Jürgen Greifeneder, François Cellier

  10. Thank you. Jürgen Greifeneder, François Cellier

  11. Gas Phase CF CF Gas liq 3 3 3 3 Ø CD, DVA, Condensation (and Evaporation) Ø 3 3 3 CD, DVA Transition element Transition element Phase- boundary 3 3 3 3 Ø CD, DVA, Evaporation (and Condensation) 3 Ø 3 3 CF CF Fluid Phase gas liq Modeling Air Bubbles Jürgen Greifeneder, François Cellier

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